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Conventional DEA performs like a “black box” and provides no information about sub-processes. In some cases, such as banks, providing services made up of interactive and interdependent processes. Also, in real-world applications, inputs could be shared among these sub-processes. Moreover, due to the characteristics of some variables, such as number of employees, only integer values could be assigned to them. Hence, to address these shortcomings, in this study, a mixed-integer network DEA (MI-NDEA) with shared inputs and undesirable outputs has been proposed to evaluate the efficiency of decision-making units. The proposed model considers integer values for some of the input variables. Also, it assumes that some inputs are shared among different stages of the production process. To illustrate the capability of the model, the efficiency of “Internet banking”, “profitability”, “production”, and “overall” performance of a set of bank branches have been evaluated and results are discussed. The results indicate that the mean of overall efficiency for all branches is high. However, some branches are not efficient enough in the “Production” stage or “Profitability” stage. To identify the source of inefficiency in such branches, projection values have been calculated and recommendations have been made for policy makers.

A mixed-integer network DEA with shared inputs and undesirable outputs for performance evaluation: Efficiency measurement of bank branches